Question: If $x \odot y = 4x^{2}-y^{2}$ and $x \triangleleft y = xy+4x-y$, find $3 \odot (2 \triangleleft -6)$.
First, find $2 \triangleleft -6$ $ 2 \triangleleft -6 = (2)(-6)+(4)(2)-(-6)$ $ \hphantom{2 \triangleleft -6} = 2$ Now, find $3 \odot 2$ $ 3 \odot 2 = 4(3^{2})-2^{2}$ $ \hphantom{3 \odot 2} = 32$.